Simplifying Fractions to Lowest Terms

Mastering the Art of Fraction Reduction

Demonstrator: Alex Yuan

Year 4 Mastery & Competition Foundation • Think Academy Australia

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🍕 The Pizza Slicing Riddle: Who Ate More?

Tom: 4 of 6 Slices

46 of Pizza

=

Jerry: 2 of 3 Slices

23 of Pizza

🤔 Who Ate More Pizza?

Tom: 4 slices

vs

Jerry: 2 slices

Look at the shaded area — they cover the exact same amount!

                  ✨ Merge Slices in Pairs of 2:
                
                  4 small slices ÷ 2 = 2 big slices
                  
6 total slices ÷ 2 = 3 big slices

                  ⚖️ Golden Law of Fractions:
                
                  46
                  =
                  4 ÷ 26 ÷ 2
                  =
                  23
                
                  Divide top and bottom by the same number — value never changes!

🔍 What is "Simplest Form"? & Your 3 Superpowers

🎯 When is Our Job Finished?

A fraction is in Simplest Form when top and bottom share NO common factors except 1!

Why is 23 in simplest form?

Factors of 2: 1, 2 | Factors of 3: 1, 3
Shared Common Factor: Only 1!

✅ 2 and 3 are COPRIME → Simplest Form Locked!

⚡ 3 Divisibility Superpowers:

Spot what to divide by in 3 seconds:

1. The Even Test (÷ 2)

Ends in 0, 2, 4, 6, 8 → divide by 2!

2. The Digit-Sum Test (÷ 3)

Sum of digits in 3-times table → divide by 3!

3. The 0 & 5 Test (÷ 5)

Ends in 0 or 5 → divide by 5!

🧠 Test 2, 3, then 5 — no guessing!

⚡ Practice 3: Detective Walkthrough (Part 1)

Question (1)

Simplify to lowest terms:

1618 = ? 16 ÷ 218 ÷ 2 = 89

💡 Consecutive numbers (8 & 9) → Always Coprime! 🎯

Question (2)

Simplify to lowest terms:

1022 = ? 10 ÷ 222 ÷ 2 = 511

💡 Both 5 & 11 are Prime → Coprime! 🎯

Question (3)

Simplify to lowest terms:

2026 = ? 20 ÷ 226 ÷ 2 = 1013

💡 13 is Prime (doesn't divide 10) → Coprime! 🎯

🚨 Question (4): The Big Boss & The Classic Trap!

Question (4) — The Big Boss

Simplify to lowest terms:

3048 = ? 30 ÷ 248 ÷ 2 = 1524

🔍 Digit-Sum Check: 1 + 5 = 6 | 2 + 4 = 6

Both numbers still divide by 3!

1524 = 15 ÷ 324 ÷ 3 = 58 🎯 DONE!

Master Shortcut

⚡ The One-Step Giant Leap:

÷ 2 then ÷ 3 = ÷ 6 in one leap!

3048 = 30 ÷ 648 ÷ 6 = 58

🚀 Stepping stones (÷2, ÷3) or Giant Leap (÷6) → Same peak: 58!

🏆 The 3-Step Master Recipe for Fractions

1

Spot Common Factors

Use divisibility superpowers:
÷ 2 (evens) • ÷ 3 (sum) • ÷ 5 (0 or 5)

2

Divide Fairly

The Golden Law:
Divide top and bottom by the exact same number!

3

Check Coprime

Never stop too early!
Finish when top and bottom share only 1!